Comments for Rationalize the Numerator of {∛(4b²)}/4

You can remove the radical from the numerator in your problem [∛(4b²)] by multiplying the numerator by itself two more times: [∛(4b²)]*[∛(4b²)]*[∛(4b²)] = 4b²

However, in order to preserve the value of the original fraction, both the numerator and denominator must each be multiplied by the same amount: [∛(4b²)].

To apply this concept, multiply the original fraction by [∛(4b²)] / [∛(4b²)] * [∛(4b²)] / [∛(4b²)] . The fraction [∛(4b²)] / [∛(4b²)] is equal to 1, so the original fraction is merely being multiplied by 1. As you can see by the following illustration, the value of the original fraction has not been changed.

= [original fraction]

= [original fraction] * [∛(4b²)] / [∛(4b²)] * [∛(4b²)] / [∛(4b²)]

= [original fraction] * 1 * 1

= [original fraction]

Therefore,

= [original fraction] * 1 * 1

= {[∛(4b²)] / 4} * 1 * 1

= {[∛(4b²)] / 4} * {∛(4b²) / ∛(4b²)} * {∛(4b²) / ∛(4b²)}

= [∛(4b²) / 4] * [∛(4b²) / ∛(4b²)] * [∛(4b²) / ∛(4b²)]

Multiply all three numerators and multiply all three denominators, just as you would when multiplying any three fractions:

= [∛(4b²) * ∛(4b²) * ∛(4b²)] / [4 * ∛(4b²) * ∛(4b²)]

It is sometimes easier to convert the radical signs to fractional exponents, and then work with the exponents. It is not necessary, but you may find it convenient.

= [(4b²)⅓ * (4b²)⅓ * (4b²)⅓] / [4 * (4b²)⅓ * (4b²)⅓]

Add the exponents as shown. As you can see, the fractional exponent (the cube root) in the numerator disappears.

= (4*b²)⅓+⅓+⅓ / [4 * (4b²)⅓+⅓]

= (4*b²)1 / [4 * (4b²)⅔]

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Sep 04, 2012

Rationalize the Numeratorby: Staff

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Part II

The factor (4) in the numerator will cancel the (4) in the denominator.

= (4*b²) / [4 * (4b²)⅔]

= (4 / 4) * [b² / (4b²)⅔]

= (4 / 4) * [b² / (4b²)⅔]

= (1) * [b² / (4b²)⅔]

= b² / (4b²)⅔

= b² / (2²b²)⅔

When evaluating an exponent of an exponent, multiply the exponents.

= b² / (2(2*⅔)) * b(2*⅔))

= b² / (2(4/3) * b(4/3))

= b² / 21+⅓b1+⅓

= b² / (21 * 2⅓ * b1 * b⅓)

= b² / (2b * 2⅓ * b⅓)

The factor (b) in the numerator will cancel the (b) in the denominator.